A Decomposition Framework for Certifiably Optimal Orthogonal Sparse PCA
Sparse Principal Component Analysis (SPCA) is an important technique for high-dimensional data analysis, improving interpretability by imposing sparsity on principal components. However, existing methods often fail to simultaneously guarantee sparsity, orthogonality, and optimality of the principal components. To address this challenge, this work introduces a novel Sparse Principal Component Analysis (SPCA) algorithm called \textsc{GS-SPCA} (SPCA with Gram-Schmidt Orthogonalization), which simultaneously enforces sparsity, orthogonality, and optimality. However, the original GS-SPCA algorithm is computationally expensive due to the inherent $\ell_0$-norm constraint. To address this issue,...
| Authors | Difei Cheng, Qiao Hu |
|---|---|
| Primary category | cs.LG |
| Published | 1 March 2026 |
| Last updated at source | 1 March 2026 |
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